dorsal/arxiv
View SchemaA Planetary System with an Escaping Mars
| Authors | Áron Süli, Rudolf Dvorak |
|---|---|
| Categories | |
| ArXiv ID | physics/0508142 |
| URL | https://arxiv.org/abs/physics/0508142 |
| DOI | 10.1002/asna.200610660 |
Abstract
The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at $\kappa_E \in (4,6)$, where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different 'Solar Systems' clarified that including only Jupiter and Saturn with their actual masses together with a more 'massive' Earth ($4 < \kappa_E < 6$) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace-Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window.
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"abstract": "The chaotic behaviour of the motion of the planets in our Solar System is\nwell established. In this work to model a hypothetical extrasolar planetary\nsystem our Solar System was modified in such a way that we replaced the Earth\nby a more massive planet and let the other planets and all the orbital elements\nunchanged. The major result of former numerical experiments with a modified\nSolar System was the appearance of a chaotic window at $\\kappa_E \\in (4,6)$,\nwhere the dynamical state of the system was highly chaotic and even the body\nwith the smallest mass escaped in some cases. On the contrary for very large\nvalues of the mass of the Earth, even greater than that of Jupiter regular\ndynamical behaviour was observed. In this paper the investigations are extended\nto the complete Solar System and showed, that this chaotic window does still\nexist. Tests in different \u0027Solar Systems\u0027 clarified that including only Jupiter\nand Saturn with their actual masses together with a more \u0027massive\u0027 Earth ($4 \u003c\n\\kappa_E \u003c 6$) perturbs the orbit of Mars so that it can even be ejected from\nthe system. Using the results of the Laplace-Lagrange secular theory we found\nsecular resonances acting between the motions of the nodes of Mars, Jupiter and\nSaturn. These secular resonances give rise to strong chaos, which is the cause\nof the appearance of the instability window.",
"arxiv_id": "physics/0508142",
"authors": [
"\u00c1ron S\u00fcli",
"Rudolf Dvorak"
],
"categories": [
"physics.class-ph",
"physics.space-ph"
],
"doi": "10.1002/asna.200610660",
"title": "A Planetary System with an Escaping Mars",
"url": "https://arxiv.org/abs/physics/0508142"
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